A329273 a(1)=1. If n is prime, a(n)=0; if not, a(n) = (the smallest prime number greater than n) minus (the largest prime number smaller than n) minus 1.

1, 0, 0, 1, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3

Offset

1,8

Comments

When n is not a prime number, a(n) expresses the size of the prime gap to which n belongs.

Links

Table of n, a(n) for n=1..100.

Formula

a(1)=1. If n is prime, a(n)=0; if not, a(n) = nextprime(n) - precprime(n) - 1.

The nonzero terms are one less than the nonzero terms of A072680. More precisely, a(n) = A072680(n) - sign(A072680(n)) for n > 1. - Rémy Sigrist, Nov 30 2019

Example

Let n=9. The smallest prime number, greater than 9 is 11, the largest prime number, smaller than 9 is 7. a(9)=11-7-1=3.

Mathematica

Array[Which[# == 1, 1, PrimeQ@ #, 0, True, Prime[# + 1] - Prime@ # - 1 &@ PrimePi@ #] &, 105] (* Michael De Vlieger, Nov 18 2019 *)

Prog

(PARI) a(n) = if (n==1, 1, if (isprime(n), 0, nextprime(n+1) - precprime(n-1) - 1)); \\ Michel Marcus, Dec 01 2019

Crossrefs

Cf. A072680, A151799, A151800.

Sequence in context: A265466 A002073 A247093 * A130719 A143606 A126660

Adjacent sequences: A329270 A329271 A329272 * A329274 A329275 A329276

Keyword

nonn

Author

Todor Szimeonov, Nov 11 2019

Status

approved